Advanced computation of the robustness margin

When applying μ analysis, the use of a frequency gridding may reveal unreliable in the specific context of narrow and high peaks on the μ plot (typically in the case of uncertain lightly damped systems). A solution for avoiding this gridding is to transform the problem into an augmented μ problem, in which the frequency is treated as an additional uncertainty. Two problems are considered: 1) the direct computation of the maximal structured singular value over an interval [ω_,ω¯] (direct approach); and 2) given a frequency ω_ and a level K of uncertainty, compute the maximal value of ω¯, such that the robustness margin inside [ω_, ω¯] is greater than K (dual approach). A skewed μ problem is obtained, in which the frequency is treated as a one-sided uncertainty. A generalized μ upper bound is proposed as a solution to this problem. Finally, we illustrate on a classical example that an efficient solution for computing the robustness margin combines the direct and dual approaches with a frequency gridding